I've only been taking hydrometer readings on my last couple of batches, and a question has been nagging me: My understanding is that, in simple terms:

Alcohol = First Reading-Final Reading

(this is simplified; please don't get too wrapped up in the definitions)

So it seems to me that the OG effectively sets a maximum on the alcohol content. How can this be, when I can add more sugar at bottling, and create more alcohol?

For example, last night I brewed a batch of wheat beer, and took an OG reading of 1.05. So when I bottle, the lowest reading I can get is 1.00, meaning I'll have a max of .05. How can this be, when I can add a boatload of sugar? Does the sugar in the second stage get somehow limited by the original gravity?

The gravity of your wort/beer goes back up if you add more sugar (or extract). The O.G. is not a limiting factor, as it is just a measurement of how much sugar is in solution just after the boil. You could raise the gravity right then by adding sugar or you could let the gravity fall (heavier sugar gets turned into lighter alcohol) then add sugar and bring the gravity back up to whatever.

But in a way, if you don't add additional fermentable sugar then there is a limit to the amount of alcohol you're gonna get. I've never heard of a beer that has an F.G. lower than 1.0, but that number is not a hard limit on anything. Wine, for instance, has a high enough alcohol percentage (and enough alcohol in relation to unfermented sugars) that it usually falls below 1.0. Beer usually finishes higher because beer yeast does not ferment out as completely as wine yeast.

OP, the forumla for figuring alcohol by volume is (OG - FG) * 131. This is approximate (I actually use 131.25, but that's close enough).

So if your beer is 1.050 and ferments down to 1.013, your ABV is ~ 4.85%.

If you think about this, it makes perfect sense. The sugars in your beer are converted to CO2 and ethanol by the yeast. The more sugars there are to start with (OG) and the fewer sugars are left when done (FG) influence how much alcohol is in the beer.

As for adding sugar at bottling - that is negligible compared to pounds and pounds of grains and sugars.